Dimensional Quantum Chromodynamics Research Articles

Preparations for quantum simulations of quantum chromodynamics in 1+1 dimensions. I. Axial gauge

Tools necessary for quantum simulations of $1+1$ dimensional quantum chromodynamics are developed. When formulated in axial gauge and with two flavors of quarks, this system requires 12 qubits per spatial site with the gauge fields included via nonlocal interactions. Classical computations and $D$-wave's quantum annealer advantage are used to determine the hadronic spectrum, enabling a decomposition of the masses and a study of quark entanglement. Color ``edge'' states confined within a screening length of the end of the lattice are found. IBM's seven-qubit quantum computers, ibmq_jakarta and ibm_perth, are used to compute dynamics from the trivial vacuum in one-flavor QCD with one spatial site. More generally, the Hamiltonian and quantum circuits for time evolution of $1+1$ dimensional $SU({N}_{c})$ gauge theory with ${N}_{f}$ flavors of quarks are developed, and the resource requirements for large-scale quantum simulations are estimated.

Fermionic Spinon Theory of Square Lattice Spin Liquids near the Néel State

Quantum fluctuations of the N\'eel state of the square lattice antiferromagnet are usually described by a $\mathbb{CP}^1$ theory of bosonic spinons coupled to a U(1) gauge field, and with a global SU(2) spin rotation symmetry. Such a theory also has a confining phase with valence bond solid (VBS) order, and upon including spin-singlet charge 2 Higgs fields, deconfined phases with $\mathbb{Z}_2$ topological order possibly intertwined with discrete broken global symmetries. We present dual theories of the same phases starting from a mean-field theory of fermionic spinons moving in $\pi$-flux in each square lattice plaquette. Fluctuations about this $\pi$-flux state are described by 2+1 dimensional quantum chromodynamics (QCD$_3$) with a SU(2) gauge group and $N_f=2$ flavors of massless Dirac fermions. It has recently been argued by Wang et al. (arXiv:1703.02426) that this QCD$_3$ theory describes the N\'eel-VBS quantum phase transition. We introduce adjoint Higgs fields in QCD$_3$, and obtain fermionic dual descriptions of the phases with $\mathbb{Z}_2$ topological order obtained earlier using the bosonic $\mathbb{CP}^1$ theory. We also present a fermionic spinon derivation of the monopole Berry phases in the U(1) gauge theory of the VBS state. The global phase diagram of these phases contains multi-critical points, and our results imply new boson-fermion dualities between critical gauge theories of these points.

Eight dimensional QCD at one loop

The Lagrangian for a non-abelian gauge theory with an $SU(N_{\! c})$ symmetry and a linear covariant gauge fixing is constructed in eight dimensions. The renormalization group functions are computed at one loop with the special cases of $N_{\! c}$ $=$ $2$ and $3$ treated separately. By computing the critical exponents derived from these in the large $N_{\! f}$ expansion at the Wilson-Fisher fixed point it is shown that the Lagrangian is in the same universality class as the two dimensional non-abelian Thirring model and Quantum Chromodynamics (QCD). As the eight dimensional Lagrangian contains new quartic gluon operators not present in four dimensional QCD, we compute in parallel the mixing matrix of four dimensional dimension $8$ operators in pure Yang-Mills theory.

One-baryon spectrum and analytical properties of one-baryon dispersion curves in 3 + 1 dimensional strongly coupled lattice QCD with three flavors

Considering a 3 + 1 dimensional lattice quantum chromodynamics (QCD) model defined with the improved Wilson action, three flavors, and 4 × 4 Dirac spin matrices, in the strong coupling regime, we reanalyze the question of the existence of the eightfold way baryons and complete our previous work where the existence of isospin octet baryons was rigorously solved. Here, we show the existence of isospin decuplet baryons which are associated with isolated dispersion curves in the subspace of the underlying quantum mechanical Hilbert space with vectors constructed with an odd number of fermion and antifermion basic quark and antiquark fields. Moreover, smoothness properties for these curves are obtained. The present work deals with a case for which the traditional method to solve the implicit equation for the dispersion curves, based on the use of the analytic implicit function theorem, cannot be applied. We do not have only one but two solutions for each one-baryon decuplet sector with fixed spin third component. Instead, we apply the Weierstrass preparation theorem, which also provides a general method for the general degenerate case. This work is completed by analyzing a spectral representation for the two-baryon correlations and providing the leading behaviors of the field strength normalization and the mass of the spectral contributions with more than one-particle. These are needed results for a rigorous analysis of the two-baryon and meson-baryon particle spectra.

Six dimensional QCD at two loops

We construct the six dimensional Quantum Chromodynamics (QCD) Lagrangian in a linear covariant gauge and subsequently renormalize it at two loops in the MSbar scheme. The coupling constant corresponding to the gauge interaction is asymptotically free for all numbers of quark fields, Nf. Analysing the beta-functions yields a rich spectrum of fixed points. For instance, the conformal window in the six dimensional theory is at Nf = 16 for the SU(3) colour group. The critical theory structure is similar to that of an O(N) scalar theory in eight dimensions. Using the large N expansion the latter is shown to be in the same universality class as the Heisenberg ferromagnet. Similarly using the large Nf expansion, six dimensional QCD is shown to be in the same class as the two dimensional non-abelian Thirring model and four dimensional QCD. Abelian gauge theories are also renormalized at high loops in six and eight dimensions. It is shown that the gauge parameter only appears in the electron anomalous dimension at one loop, similar to four dimensions.

Large N limit of SO(N) scalar gauge theory

In this paper we study the large Nc limit of SO(Nc) gauge theory coupled to a real scalar field following ideas of Rajeev [Int. J. Mod. Phys. A 9, 5583 (1994)]. We will see that the phase space of this resulting classical theory is Sp1(H)/U(H+) which is the analog of the Siegel disk in infinite dimensions. The linearized equations of motion give us a version of the well-known ’t Hooft equation of two dimensional quantum chromodynamics.

Measurements of the deuteron elastic structure function A(Q 2) at large momentum transfers at Jefferson laboratory

Measurements of the deuteron elastic structure function A ( Q 2 ) for 0.7 ≤ Q 2 ≤ 6.0 (GeV/c) 2 are reported. The experiment performed elastic electron-deuteron scattering in coincidence, using the Hall A Facility of Jefferson Laboratory. The data are compared to theoretical models based on the impulse approximation with the inclusion of meson-exchange currents, and to predictions of quark dimensional scaling and perturbative quantum chromodynamics.

Measurements of the Deuteron Elastic Structure FunctionA(Q2)for0.7≤Q2≤6.0(GeV/c)2at Jefferson Laboratory

The deuteron elastic structure function A(Q2) has been extracted in the range 0.7≤Q2≤6.0(GeV/c)2 from cross section measurements of elastic electron-deuteron scattering in coincidence using the Hall A Facility of Jefferson Laboratory. The data are compared to theoretical models, based on the impulse approximation with the inclusion of meson-exchange currents, and to predictions of quark dimensional scaling and perturbative quantum chromodynamics.

Two dimensional quantum chromodynamics as the limit of higher dimensional theories

We define pure gauge QCD on an infinite strip of width L. Techniques similar to those used in finite TQCD allow us to relate 3D-observables to pure QCD 2 behaviors. The non triviality of the L → 0 limit is proven and the generalization to four dimensions described. The glueball spectrum of the theory in the small width limit is calculated and its evolution with L analyzed.

Two dimensional quantum chromodynamics as the limit of higher dimensional theories

We define pure gauge $QCD$ on an infinite strip of width $L$. Techniques similar to those used in finite $TQCD$ allow us to relate $3D$-observables to pure $QCD_2$ behaviors. The non triviality of the $L \arrow 0$ limit is proven and the generalization to four dimensions described. The glueball spectrum of the theory in the small width limit is calculated and compared to that of the two dimensional theory.

About the realization of chiral symmetry in QCD2

Two dimensional massless Quantum Chromodynamics presents many features which resemble those of the true theory. In particular the spectrum consists of mesons and baryons arranged in flavor multiplets without parity doubling. We analyze the implications of chiral symmetry, which is not spontaneously broken in two dimensions, in the spectrum and in the quark condensate. We study how parity doubling, an awaited consequence of Coleman's theorem, is avoided due to the dimensionality of space-time and confinement. We prove that a chiral phase transition is not possible in the theory.

THE EFFECTIVE LAGRANGIAN OF THREE DIMENSIONAL QUANTUM CHROMODYNAMICS

We consider the low energy limit of three dimensional quantum chromodynamics (QCD) with an even number of flavors. We show that parity is not spontaneously broken, but the global (flavor) symmetry is spontaneously broken. The low energy effective Lagrangian is a nonlinear sigma model on the Grassmannian. Some Chern-Simons terms are necessary in the Lagrangian to realize the discrete symmetries correctly. We consider also another parametrization of the low energy sector which leads to a three dimensional analogue of the Wess-Zumino-Witten-Novikov model. Since three dimensional QCD is believed to be a model for quantum antiferromagnetism, our effective Lagrangian can describe their long wavelength excitations (spin waves).

Variational methods in the master field formulation for (3+1)-dimensional quantum chromodynamics

Master fields are formulated for finite-$N$ (3+1)-dimensional QCD. They satisfy classical Yang-Mills equations with an infinite number of internal indices and an infinite number of constraints. Master fields and constraints on them in the large-$N$ limit ($N\ensuremath{\rightarrow}\ensuremath{\infty}$ with fixed ${g}^{2}N$) are derived from the finite-$N$ master fields and constraints using vacuum dominance among color-singlet states. Explicit solutions for the large-$N$ constraints are given and used as trial functions in a Hartree-Fock variational calculation. This Hartree-Fock method can include essential features of gluon condensation effects in the QC${\mathrm{D}}_{3+1}$ vacuum which is expected to cause confinement. Inclusion of quark fields and Hartree-Fock equations for the meson energy spectrum are also discussed.

Nonleptonic weak decays in two -dimensional quantum chromodynamics

The two-body nonleptonic decays of strange and charmed mesons are computed numerically in the framework of quantum chromodynamics in 2 dimensions using the 1/N/sub c/ expansion. It is shown that the amplitudes have no simple SU(4) algebraic properties. The decays of strange mesons are governed by the approximate ..delta..I = 1/2 rule which occurs as a consequence of the small bare masses of the s, u, and d quarks.

Hamiltonian approach to bound-state equations on a null plane in two-dimensional quantum chromodynamics

We quantize (1+1)-dimensional quantum chromodynamics on a null plane in the lightlike gauge, using a Hamiltonian formulation. Those parts of the total Hamiltonian which lead to the stringlike eigenstates of the hadrons are identified. It is seen very transparently that the 1/N expansion cannot work for baryons. The physics contained in the rest of the Hamiltonian is exhibited. It is argued that in the small-momentum region the baryon wave function must contain a gauge-invariant admixture of quark-antiquark pairs.